A symbolic nonlinear theory for network observability

The observability of a complex system refers to the property of being able to infer its whole state by measuring the dynamics of a limited set of its variables. Since monitoring all the variables defining the system’s state is experimentally infeasible or inefficient, it is of utmost importance to develop a methodological framework addressing the problem of targeting those variables yielding full observability. Despite several approaches have been proposed, most of them neglect the nonlinear nature typically exhibited by complex systems and/or do not provide the space reconstructed from the measured variables. On the one hand, since nonlinearities are often related to a lack of observability, linear approaches cannot properly address this problem. On the other hand, finding the appropriate combination of sensors (and time derivatives) spanning the reconstructed space is a very time demanding computational task for large dimensional systems. Here, we adopt a nonlinear symbolic approach taking into account the nature of the interactions among variables and analyze the distribution of the linear and nonlinear load of the variables in the symbolic Jacobian matrix of the system [1].